A cord of a circle is …

Given,
AB is equal to the radius of the circle.

In △OAB,
OA=OB=AB= radius of the circle.
Thus, △OAB is an equilateral triangle.
∠AOC=60°
Also, ∠ACB=21​∠AOB=21​×60°=30°
ACBD is a cyclic quadrilateral,
∠ACB+∠ADB=180° ∣ Opposite angles of cyclic quadrilateral
⇒∠ADB=180°−30°=150°
Thus, angle subtend by the chord at a point on the minor arc and also at a point on the major arc are 150° and 30° respectively.

A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc. 

∵ OA = OB = AB    I Given
∴ ∆OAB is equilateral.
∴ ∠AOB = 60°



| The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Now, ∵ ADBC is a cyclic quadrilateral.
∴ ∠ADB + ∠ACB = 180°
| The sum of either pair of opposite angles of a cyclic quadrilateral is 180°
⇒ ∠ADB+ 30°= 180°
⇒    ∠ADB = 180° - 30°
⇒    ∠ADB = 150°.